P(x)= -0.0013x^3+0.3x^2+8x-372. find the maximum without graphing. show step by step.

The Maximum value is

Step-by-step explanation:

Given,

(equation-1)

Differentiate above equation with respect to 'x',

--- (equation 2)

Again differentiate above equation with respect to 'x',

------- (equation 3)

From equation-2 we see,

The value of , , .

Now, for maximum or minimum, the first derivative must be 0.

For maximum,

So,

Using the quadratic formula, we find the roots of

or

For ,

Which is minimum value at

And for ,

Which is maximum value at  

Plug in equation-1,

So the Maximum value is

answer: 177/8

step-by-step explanation:

step-by-step explanation: